22-08-2012, 03:28 PM
Duration Gap Analysis
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An alternative method for measuring interest-rate risk, called duration gap analysis,
examines the sensitivity of the market value of the financial institution’s net worth to
changes in interest rates. Duration analysis is based on Macaulay’s concept of duration,
which measures the average lifetime of a security’s stream of payments (described in the
appendix to Chapter 4). Recall that duration is a useful concept, because it provides a
good approximation, particularly when interest-rate changes are small, of the sensitivity
of a security’s market value to a change in its interest rate using the following formula.
After having determined the duration of all assets and liabilities on the bank’s balance
sheet, the bank manager could use this formula to calculate how the market value
of each asset and liability changes when there is a change in interest rates and then calculate
the effect on net worth. There is, however, an easier way to go about doing this,
derived from the basic fact about duration we learned in the appendix to Chapter 4:
Duration is additive; that is, the duration of a portfolio of securities is the weighted
average of the durations of the individual securities, with the weights reflecting the proportion
of the portfolio invested in each. What this means is that the bank manager can
figure out the effect that interest-rate changes will have on the market value of net worth
by calculating the average duration for assets and for liabilities and then using those figures
to estimate the effects of interest-rate changes.
Example of a Nonbanking Financial Institution
So far we have focused on an example involving a banking institution that has borrowed
short and lent long so that when interest rates rise, both income and the net worth of
the institution fall. It is important to recognize that income and duration gap analysis
applies equally to other financial institutions. Furthermore, it is important for you to
see that some financial institutions have income and duration gaps that are opposite in
sign to those of banks, so that when interest rates rise, both income and net worth rise
rather than fall. To get a more complete picture of income and duration gap analysis, let
us look at a nonbank financial institution, the Friendly Finance Company, which specializes
in making consumer loans.
Some Problems with Income and Duration Gap Analysis
Although you might think that income and duration gap analysis is complicated
enough, further complications make a financial institution manager’s job even harder.
One assumption that we have been using in our discussion of income and duration
gap analysis is that when the level of interest rates changes, interest rates on all maturities
change by exactly the same amount. That is the same as saying that we conducted
our analysis under the assumption that the slope of the yield curve remains unchanged.
Indeed, the situation is even worse for duration gap analysis